On the vertex-distinguishing proper edge-colorings of graphs
We prove the following conjecture of Burris and Schelp: a colouring of the edges of a graph of order \(n\) such that a vertex is not incident with two edges of the same color and any two vertices are incident with different sets of colors is possible using at most \(n+1\) colors; cf. \textit{A. C. Burris} and \textit{R. H. Schelp} [J. Graph Theory 26, No. 2, 73-82 (1997; Zbl 0886.05068)].
scientific article; zbMATH DE number 1346899